6 papers · 1 filter
Marx versus Engels on infinitesimals: Chimera or triumph?
Mikhail G. Katz, Karl Kuhlemann, Semen S. Kutateladze
We document the evolution of Karl Marx's take on infinitesimals. We contrast his initial favorable stance with later criticisms, and examine the differing perspectives of Marx and…
A philosophical history of infinitesimals
Vladimir Kanovei, Mikhail G. Katz, Taras Kudryk +1
We explore the issue of providing a foundational framework for Leibnizian infinitesimals in the light of modern standard and nonstandard approaches. We outline a trichotomy of ordi…
Formalism 25
Mikhail G. Katz, Karl Kuhlemann, Sam Sanders +1
Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension b…
Leibniz's contested infinitesimals: Further depictions
Mikhail G. Katz, Karl Kuhlemann
We contribute to the lively debate in current scholarship on the Leibnizian calculus. In a recent text, Arthur and Rabouin argue that non-Archimedean continua are incompatible with…
Of pashas, popes, and indivisibles
Mikhail G. Katz, David Sherry, Monica Ugaglia
The studies of Bonaventura Cavalieri's indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri's mathematics, as well as of the mathematic…
A Leibniz/NSA comparison
Mikhail G. Katz, Karl Kuhlemann, David Sherry
We present some similarities between Leibnizian and Robinsonian calculi, and address some objections raised by historians. The comparison with NSA facilitates our appreciation of s…